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<br> <h1> Link to the source code for this example: </h1>
<a href="https://github.com/libMesh/libmesh/tree/master/examples/vector_fe/vector_fe_ex9" target="_blank">Open vector_fe_ex9 in new tab.</a>
<a name="output"></a> 
<br><br><br> <h1> The console output of the program: </h1> 
<pre>
***************************************************************
* Running Example vector_fe_ex9:
*   ./example-opt --HDG-static-condensation cavity=true mms=true element_type=TRI6 -ksp_type preonly -HDG_condensed_pc_type lu -HDG_condensed_pc_factor_shift_type NONZERO -snes_linesearch_type basic 
***************************************************************
 
 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=25
    n_local_nodes()=25
  n_elem()=8
    n_local_elem()=8
    n_active_elem()=8
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "HDG"
    Type "NonlinearImplicit"
    Variables={ "qu" "qv" } { "vel_x" "vel_y" } { "lm_u" "lm_v" } "pressure" "global_lm" 
    Finite Element Types="L2_LAGRANGE_VEC" "L2_LAGRANGE" "SIDE_HIERARCHIC" "L2_LAGRANGE" "SCALAR" 
    Approximation Orders="FIRST" "FIRST" "FIRST" "FIRST" "FIRST" 
    n_dofs()=233
    n_local_dofs()=233
    max(n_local_dofs())=233
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=233
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 7.93562
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 89
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

  NL step  0, |residual|_2 = 3.098088e+00
  NL step  1, |residual|_2 = 4.646853e-01
  NL step  2, |residual|_2 = 1.414071e-03
  NL step  3, |residual|_2 = 1.945238e-07
  NL step  4, |residual|_2 = 1.496725e-11
L2 error for u is: 1.543638e-01
L2 error for v is: 1.543638e-01
L2 error for pressure is: 2.879229e-01
 
***************************************************************
* Done Running Example vector_fe_ex9:
*   ./example-opt --HDG-static-condensation cavity=true mms=true element_type=TRI6 -ksp_type preonly -HDG_condensed_pc_type lu -HDG_condensed_pc_factor_shift_type NONZERO -snes_linesearch_type basic 
***************************************************************
***************************************************************
* Running Example vector_fe_ex9:
*   ./example-opt --HDG-static-condensation cavity=false mms=true element_type=TRI6 -ksp_type preonly -HDG_condensed_pc_type lu -HDG_condensed_pc_factor_shift_type NONZERO -snes_linesearch_type basic 
***************************************************************
 
 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=25
    n_local_nodes()=25
  n_elem()=8
    n_local_elem()=8
    n_active_elem()=8
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "HDG"
    Type "NonlinearImplicit"
    Variables={ "qu" "qv" } { "vel_x" "vel_y" } { "lm_u" "lm_v" } "pressure" 
    Finite Element Types="L2_LAGRANGE_VEC" "L2_LAGRANGE" "SIDE_HIERARCHIC" "L2_LAGRANGE" 
    Approximation Orders="FIRST" "FIRST" "FIRST" "FIRST" 
    n_dofs()=232
    n_local_dofs()=232
    max(n_local_dofs())=232
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=232
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 7.2069
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 26
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

  NL step  0, |residual|_2 = 3.909782e+00
  NL step  1, |residual|_2 = 1.058792e+00
  NL step  2, |residual|_2 = 2.515937e-02
  NL step  3, |residual|_2 = 9.010639e-05
  NL step  4, |residual|_2 = 1.295848e-08
L2 error for u is: 2.318716e-01
L2 error for v is: 3.545995e-01
L2 error for pressure is: 6.271178e-01
 
***************************************************************
* Done Running Example vector_fe_ex9:
*   ./example-opt --HDG-static-condensation cavity=false mms=true element_type=TRI6 -ksp_type preonly -HDG_condensed_pc_type lu -HDG_condensed_pc_factor_shift_type NONZERO -snes_linesearch_type basic 
***************************************************************
***************************************************************
* Running Example vector_fe_ex9:
*   ./example-opt --HDG-static-condensation cavity=true mms=false element_type=TRI6 -ksp_type preonly -HDG_condensed_pc_type lu -HDG_condensed_pc_factor_shift_type NONZERO -snes_linesearch_type basic 
***************************************************************
 
 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=25
    n_local_nodes()=25
  n_elem()=8
    n_local_elem()=8
    n_active_elem()=8
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "HDG"
    Type "NonlinearImplicit"
    Variables={ "qu" "qv" } { "vel_x" "vel_y" } { "lm_u" "lm_v" } "pressure" "global_lm" 
    Finite Element Types="L2_LAGRANGE_VEC" "L2_LAGRANGE" "SIDE_HIERARCHIC" "L2_LAGRANGE" "SCALAR" 
    Approximation Orders="FIRST" "FIRST" "FIRST" "FIRST" "FIRST" 
    n_dofs()=233
    n_local_dofs()=233
    max(n_local_dofs())=233
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=233
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 7.93562
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 89
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

  NL step  0, |residual|_2 = 1.414214e+00
  NL step  1, |residual|_2 = 9.949641e-02
  NL step  2, |residual|_2 = 4.123721e-04
  NL step  3, |residual|_2 = 2.724544e-08
  NL step  4, |residual|_2 = 1.332948e-12
 
***************************************************************
* Done Running Example vector_fe_ex9:
*   ./example-opt --HDG-static-condensation cavity=true mms=false element_type=TRI6 -ksp_type preonly -HDG_condensed_pc_type lu -HDG_condensed_pc_factor_shift_type NONZERO -snes_linesearch_type basic 
***************************************************************
***************************************************************
* Running Example vector_fe_ex9:
*   ./example-opt --HDG-static-condensation cavity=false mms=false element_type=TRI6 -ksp_type preonly -HDG_condensed_pc_type lu -HDG_condensed_pc_factor_shift_type NONZERO -snes_linesearch_type basic 
***************************************************************
 
 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=105
    n_local_nodes()=105
  n_elem()=40
    n_local_elem()=40
    n_active_elem()=40
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "HDG"
    Type "NonlinearImplicit"
    Variables={ "qu" "qv" } { "vel_x" "vel_y" } { "lm_u" "lm_v" } "pressure" 
    Finite Element Types="L2_LAGRANGE_VEC" "L2_LAGRANGE" "SIDE_HIERARCHIC" "L2_LAGRANGE" 
    Approximation Orders="FIRST" "FIRST" "FIRST" "FIRST" 
    n_dofs()=1128
    n_local_dofs()=1128
    max(n_local_dofs())=1128
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=1128
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 7.29787
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 26
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

  NL step  0, |residual|_2 = 2.449490e+00
  NL step  1, |residual|_2 = 1.148283e+00
  NL step  2, |residual|_2 = 4.624845e-02
  NL step  3, |residual|_2 = 3.055077e-04
  NL step  4, |residual|_2 = 1.646051e-08
 
***************************************************************
* Done Running Example vector_fe_ex9:
*   ./example-opt --HDG-static-condensation cavity=false mms=false element_type=TRI6 -ksp_type preonly -HDG_condensed_pc_type lu -HDG_condensed_pc_factor_shift_type NONZERO -snes_linesearch_type basic 
***************************************************************
***************************************************************
* Running Example vector_fe_ex9:
*   ./example-opt cavity=true mms=true element_type=TRI6 -pc_type lu -pc_factor_shift_type NONZERO -snes_linesearch_type basic 
***************************************************************
 
 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=25
    n_local_nodes()=25
  n_elem()=8
    n_local_elem()=8
    n_active_elem()=8
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "HDG"
    Type "NonlinearImplicit"
    Variables={ "qu" "qv" } { "vel_x" "vel_y" } { "lm_u" "lm_v" } "pressure" "global_lm" 
    Finite Element Types="L2_LAGRANGE_VEC" "L2_LAGRANGE" "SIDE_HIERARCHIC" "L2_LAGRANGE" "SCALAR" 
    Approximation Orders="FIRST" "FIRST" "FIRST" "FIRST" "FIRST" 
    n_dofs()=233
    n_local_dofs()=233
    max(n_local_dofs())=233
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=233
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 38.8369
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 233
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

  NL step  0, |residual|_2 = 3.098088e+00
  NL step  1, |residual|_2 = 4.645423e-01
  NL step  2, |residual|_2 = 1.413344e-03
  NL step  3, |residual|_2 = 3.386920e-07
  NL step  4, |residual|_2 = 4.623737e-11
L2 error for u is: 1.543638e-01
L2 error for v is: 1.543638e-01
L2 error for pressure is: 2.879229e-01
 
***************************************************************
* Done Running Example vector_fe_ex9:
*   ./example-opt cavity=true mms=true element_type=TRI6 -pc_type lu -pc_factor_shift_type NONZERO -snes_linesearch_type basic 
***************************************************************
***************************************************************
* Running Example vector_fe_ex9:
*   ./example-opt cavity=false mms=true element_type=TRI6 -pc_type lu -pc_factor_shift_type NONZERO -snes_linesearch_type basic 
***************************************************************
 
 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=25
    n_local_nodes()=25
  n_elem()=8
    n_local_elem()=8
    n_active_elem()=8
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "HDG"
    Type "NonlinearImplicit"
    Variables={ "qu" "qv" } { "vel_x" "vel_y" } { "lm_u" "lm_v" } "pressure" 
    Finite Element Types="L2_LAGRANGE_VEC" "L2_LAGRANGE" "SIDE_HIERARCHIC" "L2_LAGRANGE" 
    Approximation Orders="FIRST" "FIRST" "FIRST" "FIRST" 
    n_dofs()=232
    n_local_dofs()=232
    max(n_local_dofs())=232
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=232
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 37
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 62
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

  NL step  0, |residual|_2 = 3.909782e+00
  NL step  1, |residual|_2 = 1.058987e+00
  NL step  2, |residual|_2 = 2.516098e-02
  NL step  3, |residual|_2 = 9.010146e-05
  NL step  4, |residual|_2 = 1.877749e-09
L2 error for u is: 2.318716e-01
L2 error for v is: 3.545995e-01
L2 error for pressure is: 6.271178e-01
 
***************************************************************
* Done Running Example vector_fe_ex9:
*   ./example-opt cavity=false mms=true element_type=TRI6 -pc_type lu -pc_factor_shift_type NONZERO -snes_linesearch_type basic 
***************************************************************
***************************************************************
* Running Example vector_fe_ex9:
*   ./example-opt cavity=true mms=false element_type=TRI6 -pc_type lu -pc_factor_shift_type NONZERO -snes_linesearch_type basic 
***************************************************************
 
 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=25
    n_local_nodes()=25
  n_elem()=8
    n_local_elem()=8
    n_active_elem()=8
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "HDG"
    Type "NonlinearImplicit"
    Variables={ "qu" "qv" } { "vel_x" "vel_y" } { "lm_u" "lm_v" } "pressure" "global_lm" 
    Finite Element Types="L2_LAGRANGE_VEC" "L2_LAGRANGE" "SIDE_HIERARCHIC" "L2_LAGRANGE" "SCALAR" 
    Approximation Orders="FIRST" "FIRST" "FIRST" "FIRST" "FIRST" 
    n_dofs()=233
    n_local_dofs()=233
    max(n_local_dofs())=233
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=233
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 38.8369
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 233
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

  NL step  0, |residual|_2 = 1.414214e+00
  NL step  1, |residual|_2 = 9.961639e-02
  NL step  2, |residual|_2 = 4.125528e-04
  NL step  3, |residual|_2 = 7.831231e-08
  NL step  4, |residual|_2 = 3.726669e-12
 
***************************************************************
* Done Running Example vector_fe_ex9:
*   ./example-opt cavity=true mms=false element_type=TRI6 -pc_type lu -pc_factor_shift_type NONZERO -snes_linesearch_type basic 
***************************************************************
***************************************************************
* Running Example vector_fe_ex9:
*   ./example-opt cavity=false mms=false element_type=TRI6 -pc_type lu -pc_factor_shift_type NONZERO -snes_linesearch_type basic 
***************************************************************
 
 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=105
    n_local_nodes()=105
  n_elem()=40
    n_local_elem()=40
    n_active_elem()=40
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "HDG"
    Type "NonlinearImplicit"
    Variables={ "qu" "qv" } { "vel_x" "vel_y" } { "lm_u" "lm_v" } "pressure" 
    Finite Element Types="L2_LAGRANGE_VEC" "L2_LAGRANGE" "SIDE_HIERARCHIC" "L2_LAGRANGE" 
    Approximation Orders="FIRST" "FIRST" "FIRST" "FIRST" 
    n_dofs()=1128
    n_local_dofs()=1128
    max(n_local_dofs())=1128
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=1128
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 37.9362
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 62
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

  NL step  0, |residual|_2 = 2.449490e+00
  NL step  1, |residual|_2 = 1.148286e+00
  NL step  2, |residual|_2 = 4.624937e-02
  NL step  3, |residual|_2 = 3.054618e-04
  NL step  4, |residual|_2 = 3.047391e-08
  NL step  5, |residual|_2 = 3.399293e-12
 
***************************************************************
* Done Running Example vector_fe_ex9:
*   ./example-opt cavity=false mms=false element_type=TRI6 -pc_type lu -pc_factor_shift_type NONZERO -snes_linesearch_type basic 
***************************************************************
</pre>
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